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Truncated RAP-MUSIC (TRAP-MUSIC) for MEG and EEG Source Localization

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NeuroImage 167 (2018) 73–83 Contents lists available at ScienceDirect NeuroImage journal homepage: www.elsevier.com/locate/neuroimage Truncated RAP-MUSIC (TRAP-MUSIC) for MEG and EEG source localization Niko Makel€ a€ a,b,*, Matti Stenroos a, Jukka Sarvas a, Risto J. Ilmoniemi a,b a Department of Neuroscience and Biomedical Engineering (NBE), Aalto University School of Science, Espoo, Finland b BioMag Laboratory, HUS Medical Imaging Center, Helsinki University Hospital (HUH), Helsinki, Finland ARTICLE INFO ABSTRACT Keywords: Electrically active brain regions can be located applying MUltiple SIgnal Classification (MUSIC) on magneto- or Magnetoencephalography electroencephalographic (MEG; EEG) data. We introduce a new MUSIC method, called truncated recursively- Electroencephalography applied-and-projected MUSIC (TRAP-MUSIC). It corrects a hidden deficiency of the conventional RAP-MUSIC MEG algorithm, which prevents estimation of the true number of brain-signal sources accurately. The correction is EEG done by applying a sequential dimension reduction to the signal-subspace projection. We show that TRAP-MUSIC Source localization significantly improves the performance of MUSIC-type localization; in particular, it successfully and robustly Inverse methods locates active brain regions and estimates their number. We compare TRAP-MUSIC and RAP-MUSIC in simula- Multiple sources tions with varying key parameters, e.g., signal-to-noise ratio, correlation between source time-courses, and initial estimate for the dimension of the signal space. In addition, we validate TRAP-MUSIC with measured MEG data. We suggest that with the proposed TRAP-MUSIC method, MUSIC-type localization could become more reliable and suitable for various online and offline MEG and EEG applications. Introduction sources better, as uncorrelatedness is not assumed in defining the MUSIC localizer. Furthermore, RAP-MUSIC provides an important solu- Multiple signal classification (MUSIC) and its recursively-applied tion to the difficult peak-detection problem of the basic MUSIC, and al- version (RAP-MUSIC) are standard methods for locating active brain lows a straightforward automation of the multiple source localization regions in magneto- and electroencephalography (MEG/EEG). MUSIC- task (Mosher and Leahy, 1999). While RAP-MUSIC can be used in type source localization is based on dividing the data space into signal analyzing EEG/MEG offline for both event-related (Pascarella et al., and noise subspaces, and testing for each candidate source in the region- 2010; Cheyne et al., 2006) and spontaneous brain signals (Ewald et al., of-interest (ROI), whether its topography belongs to the signal subspace 2014; Baker et al., 2014; Groβ et al., 2001), it's computational efficiency or not Schmidt (1986); Mosher and Leahy (1999). makes it a particularly intriguing tool for online applications, such as Thanks to their simplicity/intuitiveness, computational efficiency, closed-loop EEG systems and brain–computer interfaces (Dinh et al., and insensitivity to measurement noise as well as to temporal correla- 2012, 2014; Sanchez et al., 2014; Birbaumer et al., 2009). tions between the active sources, MUSIC methods, especially RAP- However, we tested the performance of RAP-MUSIC on simulated MUSIC, have been found useful in various offline and online MEG/EEG EEG data and observed that it systematically overestimated the number applications (Mosher and Leahy, 1999; Mosher et al., 1999; Dinh et al., of the sources, i.e., it gave false positives. This raised a question whether 2012, 2014). MUSIC-framework offers probably one of the simplest in- there is something wrong or suboptimal in the conceptually beautiful verse methods that incorporates both spatial and temporal information in RAP-MUSIC. Therefore, we decided to investigate the RAP-MUSIC al- source localization from EEG/MEG (Mosher and Leahy, 1999). MUSIC is gorithm in detail. closely related to beamformers, which are extensively used in analysis of We introduce a novel recursive MUSIC-type method called truncated EEG/MEG (Sekihara and Nagarajan, 2008). One difference is that, unlike RAP-MUSIC (TRAP-MUSIC), which corrects a hidden limitation in the beamformers, MUSIC does not provide the time-courses during the conventional RAP-MUSIC algorithm. We call this limitation ’the RAP localization process; they need to be estimated separately. Unlike dilemma’. Due to the RAP dilemma, the recursive process may leave beamformer, the MUSIC procedure does not require the inversion of the unwanted residuals to the data model; these residuals can lead to high data covariance matrix. MUSIC should also tolerate time-correlated localizer values and thus to misleading interpretation of the location and * Corresponding author. Department of Neuroscience and Biomedical Engineering (NBE), Aalto University School of Science, Espoo, Finland. E-mail address: niko.makela@aalto.fi (N. Makel€ a).€ https://doi.org/10.1016/j.neuroimage.2017.11.013 Received 6 June 2017; Received in revised form 18 October 2017; Accepted 4 November 2017 Available online 8 November 2017 1053-8119/© 2017 Elsevier Inc. All rights reserved. N. Makel€ a€ et al. NeuroImage 167 (2018) 73–83 ð ; η Þ number of the sources. We explain and analyze the RAP dilemma both We assume that the columns of A, l pj j , are linearly independent, theoretically and in numerical simulations, and show how TRAP-MUSIC i.e., rankðAÞ¼n. Also, we assume that the time-courses S are time- overcomes this problem. TRAP-MUSIC is a ’corrected’ version of the centered, i.e., have zero mean, and that they are non-vanishing and lin- conventional RAP-MUSIC; TRAP-MUSIC applies a sequential dimension early independent, so that rankðSÞ¼n. Note that the time-courses may reduction to the signal-space estimate. We show that our correction al- T be correlated, i.e., si sj , where T denotes transpose, may be non-zero for lows robust and reliable estimation of the number of the sources, which is i≠j. Finally, we assume that a sufficiently accurate forward model often not possible with RAP-MUSIC. is available. New MUSIC methods have been recently developed to serve in spe- cific applications, e.g., for locating extended sources (ExSo-MUSIC (Birot et al., 2011);), or for locating synchronous activity, either by exploiting MUSIC source clustering (POP-MUSIC (Liu and Schimpf, 2006);), or the imagi- nary part of the cross-spectrum (Wedge-MUSIC; (Ewald et al., 2014), The objective of MUSIC-type methods is to estimate the source pa- SC-MUSIC (Shahbazi et al., 2015);). We point out that most of these rameters from the noisy measurement data Y (Mosher and Leahy, 1998, MUSIC variations have added their modifications on top of the conven- 1999; Schmidt, 1986) with the aid of spatial/physical information of the tional RAP-MUSIC; they first apply RAP-MUSIC, and subsequently apply forward model and temporal information of the measured time-series their novel extra step. Therefore, it is possible that at least some issues signals. In other words, one wants to find the sources, typically dipoles ð ; η Þ; …; ð ; η Þ due to the RAP-dilemma may have been inherited by methods that use p1 1 pn n . In practice, localization is done by a localizer the actual RAP-MUSIC. Contrary to these methods, our improvement is (function), which is evaluated at all source-location candidates in the not an additional step, but a correction applied within the iterative discretized scanning grid overlaid on the ROI. The maxima of the local- MUSIC algorithm. izer correspond to the estimated source locations. It is worth noticing that We compare TRAP-MUSIC with RAP-MUSIC, providing both illus- real sources are not point-like, and they are not exactly at the scanning trative examples and statistical evidence from extensive simulations with grid points—neither in practice and nor in our simulations (Kaipio and varying key parameters, e.g., SNR, number of recursion steps and tem- Somersalo, 2007). poral correlation between sources. In addition, using reader-friendly MUSIC algorithms are based on the separation of data space, span (YÞ, basic linear algebra, we give a solid mathematical justification for the into two mutually orthogonal subspaces, the signal space spanðAÞ and the ⊥ concepts on which TRAP-MUSIC is based, and demonstrate its perfor- noise space spanðAÞ ; spanðYÞ and spanðAÞ refer to vector subspaces mance on measured MEG data. spanned by the columns of Y and A, respectively. Let P ¼ AAy, where y fi sg We argue that TRAP-MUSIC is an ef cient and useful tool for is the Moore–Penrose pseudoinverse, be the orthogonal projection from revealing the active brain from MEG/EEG data. Its improvements in ℝm data space onto spanðAÞ, i.e., it is the projection to the brain- performance come without any computational cost, and thus, it is suit- signal space. fl able for both online and of ine applications (for online use of RAP- MUSIC algorithms are usually divided into two categories: scalar MUSIC, see e.g., Dinh et al. (2012, 2014)). Essentially, TRAP-MUSIC MUSIC, which is used if the orientations of the test dipoles in the ROI are should be suitable for any application where RAP-MUSIC could be predetermined and fixed for each location in the forward model, and considered, and it may open new windows for MUSIC in analysis of vector MUSIC if the dipole orientations are not predetermined or known a MEG/EEG. priori (Mosher and Leahy, 1999; Sekihara and Nagarajan, 2008; Ham€ al€ ainen€ et al., 1993). In the fixed-orientation case, the orientation η Theory and methods is a function of location p, i.e., η ¼ ηðpÞ; consequently, the topographies lðp; ηÞ¼LðpÞηðpÞ are functions of only the location p. Description of the measurement data For simplicity, consider here scalar MUSIC. Scalar MUSIC is based on the following property of the signal-space projection Psg: for any p in the We assume that the (noiseless part of the) measurement data are ROI, PsglðpÞ¼lðpÞ if lðpÞ is one of the actual source topographies that generated by a finite number of cortical sources that can be modeled by a contributed to spanðAÞ, and jjPsglðpÞjj < jjlðpÞjj otherwise; k : k denotes set of equivalent current dipoles (Ham€ al€ ainen€ et al., 1993).
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